1. Conic Sections in Polar Coordinates
Lesson 10.6

2. Definition of Parabola
Set of points equal distance from a point and a line
Point is the focus
Line is the directrix
If the ratio of the two distances is different from 1, other curves result •

3. General Definition of a Conic Section
Given a fixed line L and a fixed point F
A conic section is the set of all points P in the plane such that F •
d(P, F) •
d(P, L) L
Note: This e stands for eccentricity.
It is not the same as e =

4. General Definition of a Conic Section
When e has different values, different curves result
0 < e < 1 The conic is an ellipse
e = 1 The conic is a parabola
e > 1 The conic is a hyperbola
Note: The distances are positive
e is always greater than zero

5. Polar equations of Conic Sections
A polar equation that has one of the following forms
is a conic section
When cos is used, major axis horizontal
Directrix at x = p
When sin is used, major axis vertical
Directrix at y = p

6. Note the false asymptotes
Example
Given
Identify the conic
What is the eccentricity?
e = ______
Graph the conic
Note the false asymptotes

7. Special Situation Consider Now graph Note it is rotated by -π/6
Eccentricity = ?
Conic = ?
Now graph
Note it is rotated by -π/6

8. Finding the Polar Equation
Given directrix y = -5 and e = 1
What is the conic?
Which equation to use?
5 • 1
y = - 5

9. Assignment
Lesson 10.6
Page 438
Exercises 1 – 19 odd